Geometry and Its ApplicationsElsevier, 21.02.2006 - 560 Seiten Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. - Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns - Physics - Robotics - Computer vision - Computer graphics - Stability of architectural structures - Molecular biology - Medicine - Pattern recognition - Historical notes included in many chapters |
Inhalt
| 1 | |
| 37 | |
| 103 | |
| 143 | |
5 Vectors in Geometry | 199 |
Isometries and Matrices | 257 |
Similarity Inversion and Projection | 311 |
8 Graphs Maps and Polyhedra | 379 |
Bibliography | 459 |
Answers to OddNumbered Exercises | 463 |
Index | 523 |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
algorithm angle sum apply axis bisector called central similarity circle of inversion collinear combinatorial structure components connecting contradiction coordinates corresponding cross curve definition diagonals direction vector distance draw edge end effector equations Euclidean geometry example Exercises Marks challenging exterior angle face coloring formula fullerene geodesic gives glide reflection graph Hamilton circuit Hint horizontal hyperbolic geometry image plane infinite face interior intersection isometry length line segment list coloring Marks challenging exercises mathematics matrix measure moves opposite origin parallel axiom parallel projection parametric equations perpendicular perspective projection pixels planar map polygon polyhedra polyhedron position vector previous exercise problem proof of Theorem prove quadrilateral radius robot rotation Section shortest path sides sphere spherical geometry spherical triangle spline strip pattern Suppose symmetry three-dimensional transformation translation triangle ABC vertex coloring vertices Voronoi diagram world frame y-vector
Beliebte Passagen
Seite 110 - If I commenced by saying that I am unable to praise this work (by JOHANN), you would certainly be surprised for a moment. But I cannot say otherwise. To praise it, would be to praise myself. Indeed the whole contents of the work, the path taken by your son, the results to which he is led, coincide almost entirely with my meditations, which have occupied my mind partly for the last thirty or thirtyfive years.
Seite 19 - It was the habit of the Epicureans, gays Proclus, to ridicule this theorem as being evident even to an ass and requiring no proof, and their allegation that the theorem was
Seite 44 - The sum of the measures of the angles of a triangle is 180°.
Seite 110 - If you have really succeeded, it is right that no time be lost in making it public, for two reasons: first, because ideas pass easily from one to another who can anticipate its publication; and secondly, there is some truth in this, that many things have an epoch in which they are found at the same time in several places, just as the violets appear on every side in spring.
Seite 80 - ... prove that BAEC is a parallelogram that is specifically a rectangle with consecutive sides congruent, namely a square. Statement 1.
Seite 4 - ... c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Seite 327 - Theorem, which says that the measure of an "exterior angle" of a triangle equals the sum of the measures of the two "remote interior angles," so x = y + z and w = (z - 1) + (y + 1) =y + z- Therefore, w = x.
Seite 42 - June, 1893. 1. Prove that if the diagonals of a quadrilateral bisect each other the figure is a parallelogram. 2. Prove that in any right-angled triangle the square on the side opposite to the right angle is equal to the sum of the squares on the other two sides. A purely geometrical proof is preferred. State fully each principle employed in the proof. 3. Given a straight line AB...
Seite 33 - The volume of a rectangular parallelepiped is equal to the product of its three dimensions.
Seite 151 - The diagram indicates why the triangle inequality is the analytic equivalent of the geometric proposition that one side of a triangle is shorter than the sum of the other two sides.
Verweise auf dieses Buch
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